



 
Hi Leanne, I can help you get started. Let's say one time unit is the time required to make 3 big widgets. This is also the time required to make 5 small widgets. Thus in 1 time unit the machines make 3 big plus 5 small widgets. I want to convert this to mass of small widgets but I have 3 big widgets and I know the conversion for 2 big widgets and this is going to give me fractions since 2 doesn't divide 3 evenly. To get around this I want to look at 2 time units. In 2 time units the machines make 6 big plus 10 small widgets. Now you have 3 pairs of big widgets and each pair has the same mass as 3 small widgets. Hence the 6 big widgets has the mass of 9 small widgets and hence in 2 time units the two machines have produced widgets with a total mass of 9 + 10 = 19 small widgets. How many of these double time units are needed to produce a mass of 380 small widgets? How many widgets of each kind are produced? I hope this helps,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 